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I'm playing a piece at the moment and it is in the key of A Major. A few bars in we encounter an F double sharp (F## or Fx). Would that bring the note up to G like normal, or because the Key Signature already contains an F#, does it become a G#. Just to clear up, there are no F naturals before this point.

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Imagine a single sharp written before the F#: it wouldn't have any effect (unless it cancels a natural sign in the same bar). So the double sharp raises the F# by a semi-tone, which is enharmonically equivalent to a G.

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Accidentals are always just what they say, and not affected in any way by the key signature. (Other than the key signature being the reason to put them there!)

So yes, in this case, it is an F double sharp - or G natural.

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